The paper deals with descriptor systems of the form \(E\dot x=Ax+Bu\), \(y=Cx\), with \(E\) being a singular matrix, \(x\), \(u\) and \(y\) are respectively the state, input and output vector. Compensator design for such descriptor system consists of the construction of a control law \(u=Kz+v\) with \(z\) the observer-state satisfying \(E\dot z=[A-LC]z+Bu+Ly\). By assuming the singular system to be strongly observable and strongly controllable the compensator design can be achieved in a stable manner, i.e. both the eigenvalues of \([sE-A-BK]\) as well \([sE-A+LC]\) are located arbitrarily. In order that the resulting observer dynamics is well defined, one needs to assure that the matrix \([sE-A-BK+LC]\) is regular (i.e. has a nonzero determinant). It is proven that pole assignment for both controller and observer, and regularity of the resulting observer dynamics is possible by a suitable selection of \(K\) and \(L\).